An important part of game theory is that the payoffs of a one-off game may differ if it were repeated (especially if infinitely or indefinitely). A nice illustration of that can be found here.
In a one-off game, getting $1 beats getting 50c. But taking $1 ends the game, whereas if the boys keeps taking 50c then he gets another chance to play (indefinitely), allowing him to win much more over time.
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